Problem: Solve for $x$ : $5x^2 - 5x - 100 = 0$
Solution: Dividing both sides by $5$ gives: $ x^2 {-1}x {-20} = 0 $ The coefficient on the $x$ term is $-1$ and the constant term is $-20$ , so we need to find two numbers that add up to $-1$ and multiply to $-20$ The two numbers $4$ and $-5$ satisfy both conditions: $ {4} + {-5} = {-1} $ $ {4} \times {-5} = {-20} $ $(x + {4}) (x {-5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 4) (x -5) = 0$ $x + 4 = 0$ or $x - 5 = 0$ Thus, $x = -4$ and $x = 5$ are the solutions.